Epitrochoid 

Function: calc[EpiTrochoid] - animation of an  epitrochoid 

Calling Sequence:  

EpiTrochoid(a, b, c, N, n)
EpiTrochoidComp (a, b, c, N, n, p[1], p[2]) 

Parameters:  

a -   numbers  

N - number of `+`(`*`(2, `*`(Pi))) 

n -   number of frames
p[1], p[2] -   names
 

Description: 

  • EpiTrochoid  animates the epitrochoid traced by a point P on a spoke of a wheel of radius b as it rolls outside a circle of radius a. The distance of P from the center of the rolling wheel is c. The parametric equations are
 

x = `+`(`*`(`+`(a, b), `*`(cos, `*`(t))), `-`(`/`(`*`(c, `*`(cos, `*`(`+`(a, `-`(b)), `*`(t)))), `*`(b)))) , y = `+`(`*`(`+`(a, b), `*`(sin, `*`(t))), `-`(`/`(`*`(c, `*`(sin, `*`(`+`(a, `-`(b)), `*`(t)))), `*`(b)))) 

  • EpiTrochoidComp compares in an array two different ways of constructing an epitrochoid. Typing p[1] and  p[2] return the two plots separately
 

Examples: 

> restart: with(calc):
 

> EpiTrochoid(10,2,3,1,20);
 

Plot_2d
 

> EpiTrochoid(10,3,4,3,20);
 

Plot_2d
 

> a:=3:b:=4:c:=3.5: N:=b: n:=60:
 

> EpiTrochoidComp(a,b,c,N,n,p1,p2);
 

Plot_2d Plot_2d